The Effect of Quadrature Errors in the Numerical Solution of Two-Dimensional Boundary Value Problems by Variational Techniques
The effect of reduced integration in the Steklov eigenvalue problem
In this paper we analyze the effect of introducing a numerical integration in the piecewise linear finite element approximation of the Steklov eigenvalue problem. We obtain optimal order error estimates for the eigenfunctions when this numerical integration is used and we prove that, for singular eigenfunctions, the eigenvalues obtained using this reduced integration are better approximations than those obtained using exact integration when the mesh size is small enough.
The effect of reduced integration in the Steklov eigenvalue problem
In this paper we analyze the effect of introducing a numerical integration in the piecewise linear finite element approximation of the Steklov eigenvalue problem. We obtain optimal order error estimates for the eigenfunctions when this numerical integration is used and we prove that, for singular eigenfunctions, the eigenvalues obtained using this reduced integration are better approximations than those obtained using exact integration when the mesh size is small enough.
The effect of rounding errors on a certain class of iterative methods
In this study we are concerned with the problem of approximating a solution of a nonlinear equation in Banach space using Newton-like methods. Due to rounding errors the sequence of iterates generated on a computer differs from the sequence produced in theory. Using Lipschitz-type hypotheses on the mth Fréchet derivative (m ≥ 2 an integer) instead of the first one, we provide sufficient convergence conditions for the inexact Newton-like method that is actually generated on the computer. Moreover,...
The effect of spatial scale on predicting time series: a study on epidemiological system identification.
The efficiency of modified jackknife and ridge type regression estimators: a comparison.
The efficiency of variance reduction in manufacturing and service systems: the comparison of the control variates and stratified sampling.
The eigenvalue problem and Jacobean-like methods for its solution
The eigenvalues of Hermite and rational spectral differentiation matrices.
The elimination of quantities and the solving of systems of transcendent equations by means of differential equations
The ellipsoid method for generating normally distributed random vectors
The equivalence between the Mann and Ishikawa iterations dealing with generalized contractions.
The error estimates for the infinite element method for eigenvalue problems
The Error Norm of Gaussian Quadrature Formulae for Weight Functions of Bernstein-Szegö Type.
The error norm of Gauss-Lobatto quadrature formulae for weight functions of Bernstein-Szegö type.
The estimates for the reminder term of some quadrature formulae.
The Euler Maclaurin Expansion for the Cauchy Principal Value Integral.
The Euler-Maclaurin sum formula for an inner derivation.
The existence and uniqueness theorem in Biot's consolidation theory
Existence and uniqueness theorem is established for a variational problem including Biot's model of consolidation of clay. The proof of existence is constructive and uses the compactness method. Error estimates for the approximate solution obtained by a method combining finite elements and Euler's backward method are given.
The existence of a solution and a numerical method for the Timoshenko nonlinear wave system
The initial boundary value problem for a beam is considered in the Timoshenko model. Assuming the analyticity of the initial conditions, it is proved that the problem is solvable throughout the time interval. After that, a numerical algorithm, consisting of three steps, is constructed. The solution is approximated with respect to the spatial and time variables using the Galerkin method and a Crank–Nicholson type scheme. The system of equations obtained by discretization is solved by a version of...